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Numerical investigation of the mixed convection of a magnetic nanofluid in an annulus between two vertical concentric cylinders under the influence of a non-uniform external magnetic field

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Abstract

In the present study, the hydrothermal behavior of a magnetic nanofluid (4 vol% magnetite–water) in the annular space between two vertical circular cylinders under the influence of a linear magnetic field with negative gradient is numerically investigated. In particular, the effects of the Grashof number (1000 ≤ Gr ≤ 50,000), Reynolds number (20 ≤ Re ≤ 200), and the annulus radius ratio (1.5 ≤ Do/Di ≤ 3.5) on the hydrothermal characteristics of the magnetic nanofluid are presented in detail. The flow is assumed to be steady, incompressible, and viscous. The two-phase mixture model is used to simulate the flow and heat transfer of the magnetic nanofluid. The three-dimensional governing equations are discretized using the finite volume scheme, while the SIMPLE algorithm is employed to couple the velocity and pressure. Moreover, the second-order upwind scheme is used to discretize the convective terms of the momentum and energy equations. The results show that the skin friction coefficient on the inner and outer walls of the annuli increases and decreases, respectively, by enhancing the Grashof number as well as the ratio of the radius. It is found that the Nusselt number increases by increasing the Grashof number. In the presence of an external magnetic field with the negative gradient, the skin friction coefficient on the inner and outer walls of the annulus is enhanced by decreasing the Reynolds number.

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Abbreviations

C f :

Surface friction coefficient

C p :

Constant pressure specific heat

d :

Particle diameter

D :

Diameter

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {g}\) :

Gravitational acceleration vector

G :

Magnetic field gradient

Gr :

Grashof number

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {H}\) :

Magnetic field intensity vector

H :

Magnitude of magnetic field intensity vector

k :

Conductivity

k B :

Boltzmann constant

L :

Channel length

m :

Magnetic moment

M :

Magnetization

Nu :

Nusselt number

p :

Pressure

\(q\) :

Heat flux

r :

Radial direction

R :

Radius

Re :

Reynolds number

T :

Temperature

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {v}\) :

Fluid velocity vector

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {v}_{{{\text{dr}},{\text{p}}}}\) :

Drift velocity of magnetic nanoparticles

y :

Longitudinal direction

α :

Volume fraction

β :

Thermal expansion coefficient

θ :

Peripheral direction

µ :

Effective viscosity

µ B :

Bohr magneton

µ 0 :

Magnetic permeability in vacuum

ρ :

Density

ave:

Average

i:

Inner parameter

f:

Base fluid

m:

Mixture

o:

Outer parameter

p:

Magnetic particles

w:

Wall

0:

Inlet condition

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Authors and Affiliations

  1. Department of Mechanical Engineering, Tafresh University, Tafresh, 39518-79611, Iran

    Mohamad Hamed Hekmat & Kaveh Karimzadeh Ziarati

  2. Department of Mechanical Engineering, Persian Gulf University, Bushehr, Iran

    Marzie Babaie Rabiee

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  1. Mohamad Hamed Hekmat
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Correspondence to Marzie Babaie Rabiee.

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Hekmat, M.H., Rabiee, M.B. & Ziarati, K.K. Numerical investigation of the mixed convection of a magnetic nanofluid in an annulus between two vertical concentric cylinders under the influence of a non-uniform external magnetic field. J Therm Anal Calorim 138, 1745–1759 (2019). https://doi.org/10.1007/s10973-019-08158-z

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